EDCP 342A Unit Planning-Assignment

EDCP 342A Unit planning: Rationale and overview for planning a 3 to 4 week unit of work in secondary school mathematics

Your name: Amandeep Buttar
School, grade & course: Heritage Woods Secondary School Port Moody

Topic of unit: Circle Geometry

Preplanning questions:

(1) Why do we teach this unit to secondary school students? Research and talk about the following: Why is this topic included in the curriculum? Why is it important that students learn it? What learning do you hope they will take with them from this? What is intrinsically interesting, useful, beautiful about this topic? (150 words) The circle geometry is added in the secondary school curriculum with the aim of developing students’ previous geometry knowledge further up to higher level. Studying circle properties would increase their logical thinking and deduction skills. Also, students are required to have the knowledge of circle geometry for learning the future mathematics such as, the applications in algebra and the study of calculus etc. Importance of topic: After learning circular properties, students would be able to deeply realize the role of circular shape in their daily life. With this learning, they would not only be able to create an attractive and beautiful circular design, but also determine the missing lengths of line segments of those designs. In terms of attractiveness, the circular figure is unique and perfect design as compared to other shapes. It can also be connected to the cycles of nature such as the seasons, day and night, birth and death.

(2) What is the history of the mathematics you will be teaching, and how will you introduce this history as part of your unit? Research the history of your topic through resources like Berlinghof & Gouvea’s (2002) Math through the ages: A gentle history for teachers and others  and Joseph’s (2010) Crest of the peacock: Non-european roots of mathematics, or equivalent websites. (100 words) The date of invention of circle is unknown or not recorded in the history. Euclidean used circle as a sample space in constructing the geometry. He is also known as the "father of geometry.” The concept of circles and sphere was extremely used in the Greek Astronomy too. Greeks were the ones who first observed that the earth’s size is similar to circular shape. The invention of wheel turned out to be one of the greatest revolutions on earth, which is derived from a circle. I will use history in making the hook of my lesson interested. I will engage students by asking that,” How our life would have affected if circle based inventions were not made”?

(3) The pedagogy of the unit: How to offer this unit of work in ways that encourage students’ active participation? How to offer multiple entry points to the topic? How to engage students with different kinds of backgrounds and learning preferences? How to engage students’ sense of logic and imagination? How to make connections with other school subjects and other areas of life? (150 words) As this chapter is very visual, I will have at least two different and interesting activities in each lesson in order to encourage the students’ participation in learning. The topic would be presented to students through many entry points. Firstly, in the beginning of the lesson, student would be provided real images showing properties on the projector. Students would also be asked to provide other examples of object that travel in circular pathways. Secondly, I will include some outdoor activities in order to have student actively participate in learning. For example, I would ask students to form shapes that would show circle properties by standing in the hallway or school ground accordingly. It will also help students with different backgrounds to visualize the property clearly. Furthermore, students would be given the examples of circular shapes used in every other academic subjects. The vocabulary such as, pathways, model airplane, satellite, circular, orbit, compass etc. would also be discussed for ELL students.

(4) A mathematics project connected to this unit: Plan and describe a student mathematics project that will form part of this unit. Describe the topic, aims, process and timing, and what the students will be asked to produce. (100 words) Topic: Circle Geometry Properties Time: 2-4 hours Objective: Student would be able to identify and describe features of their design that display circle geometry concepts. Introduction: Students would be asked to sketch a design for a corporate or team logo independently. The design must be based on circles including tangents and chords. Guidelines: ·        Using geometry tool or computer tools, draw your design. ·        Measure and label all angles and lengths that demonstrate the circle properties. Students’ work should show: ·        Sketches of their design. ·        A detailed, labeled copy of their design that shows circle geometry properties. ·        Written explanations of the circle properties they used in their design. ·        A final colored copy of their design with an explanation of its purpose, if necessary.

(5) Assessment and evaluation: How will you build a fair and well-rounded assessment and evaluation plan for this unit? Include formative and summative, informal/ observational and more formal assessment modes. (100 words) My overall assessment would depend upon the following three key points: 1.                  Conceptual understandings: How do students show their understanding of circle properties by explaining and illustration? 2.                  Procedural understanding: How do students calculate the angles and length of line segments in circle diagram? 3.                  Problem solving skills: How do students select and apply their learning to solve problems? Formal assessment: I would be observing students’ learning throughout the lesson. To assess students’ understanding, I would use fist of five and exit slips techniques. Students would also be assessed on their participation in learning activities. Summative assessment: There will be unit test at the end of unit. Students would receive marks out of 40.

Elements of your unit plan:

a)  Give a numbered list of the topics of the 10-12 lessons in this unit in the order you would teach them.

Lesson	Topic
1	Exploring Angles in a circle (central and Inscribed angles)
2	Angles part 2
3	Chord Properties (review Pythagoras theorem )
4	Chord properties part 2
5	Tangent to a circle
6	Tangents part 2
7	Review
8	Review
9	Unit Test
10
(11)
(12)

b) Write a detailed lesson plan for one of the lessons which will not be in a traditional lecture/ exercise/ homework format.  Be sure to include your pedagogical goals, topic of the lesson, preparation and materials, approximate timings, an account of what the students and teacher will be doing throughout the lesson, and ways that you will assess students’ background knowledge, student learning and the overall effectiveness of the lesson. Please use a template that you find helpful, and that includes all these elements.

                           

                               Lesson Plan - Properties of Chords in a Circle

Unit: Circle Geometry                               Subject: Mathematics

Grade: 9                                                         Time: 73 minutes

Big Idea or Question for the Lesson:

·         Describe the relationship among the center of a circle, a chord, and the perpendicular bisector of the chord?

PLO foci for this lesson:

• At the end of lesson, students should be able to solve problems and justify the solution strategy using circle properties, including the perpendicular from the center of a circle to a chord bisects the chord

Objectives (SWBATs):

It is expected that students will:

1. Learn about the perpendicular from the center of circle to a chord bisects the chord.

2. Learn about the line segment that joins the center of a circle to midpoint of a chord is perpendicular to the chord and its length is the shortest distance of the chord from the center of the circle.

Assessment Plan:

• Formative: Checking understanding throughout the lesson (Observation/ fist of five) Students would also be assessed on their participation; how well they work together in a group. 
• Exit slips – check for understanding of key concepts, not for marks.

Material	Equipment
Protractors Compasses Rulers Scissors Exit slips Example worksheets. ·         Fire game activity instructions sheets	Computer Projector Power point

Adaptations

·         For ESL students or students with a less extensive vocabulary, key words would be defined. ·         During the power point presentation, instructions will be given on key terms to focus on, as well as terms being written on the board and circled throughout as they are covered. Vocabulary words: ·         Chord ·         Arc ·         Central Angle ·         Perpendicular Bisector The adaptations will also help other students who may have trouble following along. For those students appear unable to write and understand at the same time, they would be given written handouts so that they can focus on the lesson rather than filling words in.

Contingency Plan for Early Finishers

Students who finish early will be given an additional question to add to their exit slips, asking them to answer the “what are three important properties of perpendicular bisectors of chords in circles?” In the future, if students are bored or need something to do, they may be given the topic related interesting puzzle.

Time	Teacher will	Student will
5 Minutes	Introduction: ·    Showing students a sequence of pictured on the overhead projector. ·    Asking students to observe. ·    Introducing topic with questions such as, ·    What could we call the horizon? ·    How is the center of the sun related to horizon?	·    Listen to introduction and observing the pictures.
10 Minutes 20 Minutes	Activity: Goal: Investigation of relation between the center of a circle and a line segment that joins two points on the circle. Explaining the procedure: Think-Pair-Share ·    Construct then cut out a large circle. Label the Centre of the circle. ·    Choose two points A and B on the circle. Join these points to form line segment AB. Make sure AB does not go through the Centre of the circle. ·    Fold the circle so that A coincides with B. Crease the fold, open the circle, and draw a line along the fold. Mark the point C where the fold line intersects AB. ·    Repeat the steps above for two other points D and E on the circle. ·    What do you notice about line segments AC and CB? ·    Compare your results with another pair of classmates. ·    What appears to be true about each line segment and its related fold line? ·    What name could you give each fold line? ·    Through which point do both fold lines appear to pass? Teaching Chord properties with examples: ·         Discussion of activity questions. ·         Example worksheets handout. ·         The teacher solves examples by engaging students in the discussion. ·         Reinforcing the correct application of the Pythagorean Theorem.	·    Turn to the person(s) next to them and perform the activity Write down answers in their notes handout and compare with another pair of students. ·    Provide answers for the teacher to write on the board ·    Listen to teacher’s definitions and answers ·    Answer any additional questions
15 Minutes	Practice: Asking students to Solve questions p.389 #1, 2, 4, 5, 6,	Students solve questions independently.
15 Minutes	Activity: Sticks on a Fire Game: ·    Dividing students into pairs. ·    Handing out activity instructions and Fire circles sheets. ·    Monitoring the activity.	Play games in pairs
8 Minutes	Closing the lesson:  Exit Slip ·         Hand out exit slip ·         In your own words, define the following questions: ·         Describe how you know that the diameter of the circle forms a right angle with the chord at their point of intersection. ·         What is perpendicular bisector of a Chord?    Home work: They would also be assigned to solve questions 7-9, 12, 13 on page 389 from the textbook. Unfinished questions from practice would also be added in the homework.	Record key points of the lesson.

Reflection / Follow Up / Next Steps:

·         Do students have a good understanding of the key terms? Does this provide a solid foundation on which to build further discussion of circle geometry? ·         Were students engaged? ·         Were they able to keep up with the speed of the presentation? ·         Were they more willing to discuss with their partners than with the class? ·         Were there students who were visibly confused or bored? ·         Were students more or less able to grasp the key points of the presentation or was it too sophisticated/fast?

Mason's Article

1) Do Mason's ideas might connect with inquiry-based learning in secondary school mathematics? (And why or why not?)

Undoubtedly, Mason’s concept of questioning will connect with inquiry based learning in secondary school mathematics. As per my knowledge, inquiry based learning heavily relies on the ideas that engage both educators and students in evidence based learning. The educator engages the students in inquiry based learning by posing a sequence of suitable questions. Consequently, the effectiveness of inquiry based learning appears to be depending upon the appropriateness of the questions that the educator asks to students in a classroom. The appropriateness of questions further depends upon many factors that are mentioned in Mason’s article. For example, I found Mason’s article perfectly answering the following questions about what to consider before posing a question to students.

What types of questions need to be asked?

How would this question help students to participate in learning rather than being obstacle in participation?

When to ask the question?

How many questions need to be asked? How many are too many?

How often the questions need to be asked?

How challenge-able my questions are?

Is my question confusing students?

How to acknowledge students' fully or partially wrong answers in the way the student does not get discouraged?

Mason’s article offers lot of information about how different ways of posing different types of questions can have positive and negative impacts on the students' learning. For example, on the one side, choosing a simple question can limit students’ ability of dealing with unfamiliar challenges. However, on the other hand, a question with reasonable challenge can provide students an opportunity to face the tough situation and then get over it successfully with good planning and approach. Additionally, the idea of asking questions as inquiring seems to be fully connected with inquiry based learning. For instance, asking as asking involves student centered learning whereas asking as telling is more teacher centered as this is what teacher wants to listen. Mason also considers questions as interventions in the progression of students' learning. He furthers says that the too much frequency and quantity of these interventions could result students relying more on their teachers instead of developing their resilience and resourcefulness. Finally, the idea of taking every discussion as a conjecture that would later be verified and justified appears to be the most effective way to encourage and engage students who are certain or uncertain in the classroom learning.

 2) How might Mason's ideas about questions in math class be incorporated into your unit planning for your long practicum?

As per my observation so for, the questioning especially in teaching of mathematics plays very vital role in not only engaging the students in learning, but also getting them ready for new learning through good connections.  Mason’s ideas about questionings can be included in the unit plans. These ideas can be very helpful in making the hook and discussion of a lesson interested and effective. Mason’s ideas inform us two types of approaches in making the questions. For example, one approach “deep end” that suggests students would demonstrate their abilities to deal with complex problems whereas the “shallow end” relies on a “staircase” theory, which includes a sequence of simple but unavoidable steps that move toward complexity of the lesson. Well, choosing a either approach or mix of both could be challenge for educator unless you are very familiar with your students’ learning abilities. I would assess my students’ learning abilities very carefully before selecting either approach.

Additionally, during the discussion of any topic, the way of questioning could significantly affect the overall students’ learning. For example, as Mason says that asking simple questions could let the students to develop poor problem solving skills in contrast to asking questions with reasonable challenge. Solving the problem in steps on the white board through the discussion of challenge-able questions could be incorporated in the unit planning as it provides students an opportunity to experience of how to resolve tough situations.